# Discrete Optimization Problem (VRP)

Consider the following setting : We have two pickup nodes (a) and (b)and two delivery nodes (c) and (d). At each pickup node, there are entities to be picked up and delivered by cars (n cars) to either (c) or (d) according to the entity type. Entities have only two types (c or d) regarding their destination. For example, a car can pick both entity types from (a) and deliver them to (c) and (d). Assume there are only two potential locations to place the car fleets (f) and (g). Where to place the fleet and What is the minimum number of cars needed to deliver all entities (each type to its destination) in the shortest time possible ?

I'm trying to formulate this problem, I've read on Vehicle Routing Problem but it seems a bit different as a vehicle is either departing from the depot empty and only picking entities along the path and bring them back to the depot or departing full of entities from the depot and dropping them off along the way.

Could anyone please guide me toward a problem class in the literature that's very close to this problem? All suggestions are highly welcomed and appreciated.

• I'm assuming the cars must have some capacity limit and travel time? In that case it seems ill-posed to minimize the number of cars and and the amount of time taken simultaneously. – Math1000 Feb 27 '16 at 1:26
• I may be wrong, but this does not look like an extremely difficult problem. I suspect this could be done in a spreadsheet. – Erwin Kalvelagen Mar 6 '16 at 17:58